Towards systematic random process representation: Bimodal PSDs characterized by bandwidth indices

Spectral approaches based on power spectral density (PSD) analysis are widely used for fatigue assessment of flexible structures due to their computational efficiency and statistical reliability. However, their accuracy depends on representative PSD datasets, which are often defined arbitrarily and fail to capture the diversity of real response shapes. This study introduces a systematic methodology to generate a minimal yet representative set of PSDs for vibration fatigue analysis. The approach models PSDs using simple rectangular bimodal shapes, described by three independent parameters and directly linked to classical bandwidth indices. This formulation provides a compact representation of structural responses while ensuring equivalence in fatigue damage rather than frequency content. Validation against sample stress PSDs from finite element models demonstrates that the bimodal approximation reproduces both cycle amplitude distributions and damage potentials with consistency comparable to established spectral methods. The proposed framework enables a more robust definition of representative load cases and supports the development and evaluation of fatigue assessment tools under realistic conditions.